Cohen was at the helm when shuttle flights resumed nearly three years later and continued to lead the center until 1993. He resigned from NASA to teach at Texas A&M University, his alma mater.
"His engineering expertise and rigor were tremendous assets to our nation and NASA," NASA Administrator Charles Bolden said in statement. "Aaron provided the critical and calm guidance needed at the Johnson Space Center to successfully recover from the Challenger accident and return the space shuttle to flight. We will miss him as a colleague, mentor and a friend."
Cohen, a mechanical engineer, joined NASA in 1962 and managed the computer guidance systems for the Apollo command module and the landing module that first carried astronauts to the moon's surface. He was a leader in developing the shuttle.
"He was the one person at the Johnson Space Center responsible for the design, development, tests and the funds -- the budget of the shuttle -- from the time it started to the time it flew," his supervisor and friend Christopher Kraft told the Houston Chronicle.
"Everybody looked up to Aaron."
Cohen died Feb. 25, NASA said. He was buried March 1 in San Antonio.